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arXiv:hep-lat/9212013 · Physics Letters B

Finite-size effects in the interface of the 3D Ising model

Michele Caselle, Ferdinando Gliozzi, S Vinti

Published Mar 1, 1993• 23 citations
arXivHTMLPDF
DOI
10.1016/0370-2693(93)90638-x

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The interface between domains of opposite magnetization in the 3D Ising model near the critical temperature displays universal finite-size effects which can be described in terms of a gaussian model of capillary waves. It turns out that these finitesize corrections depend rather strongly on the shape of the lattice. This prediction, which has no adjustable parameters, is tested and accurately verified for various lattice shapes by means of numerical simulations with a cluster algorithm. This supports also a long-standing conjecture on the finite-size effects in Wilson loops of Lattice Gauge Theories. 1
The finite-size scaling (FSS) functions for anisotropic three-dimensional (3D) Ising models of size L 1 × L 1 × aL 1 ( a : anisotropy parameter) are studied by Monte Carlo simulations. We study the a dependence of FSS functions of the Binder parameter g and the magnetization distribution function p ( m ). We have shown that the FSS functions for p ( m ) at the critical temperature change from a two-peak structure to a single-peak one by increasing or decreasing a from 1. We also study the FSS near the critical temperature of the layered square-lattice Ising model, when the systems have a large two-dimensional (2D) anisotropy. We have found the 3D and 2D FSS behaviour depending on the parameter which is fixed; a unified view of 3D and 2D FSS behaviour has been obtained for the anisotropic 3D Ising models.
By use of Monte Carlo simulations, we study the finite-size scaling (FSS) functions for anisotropic three-dimensional (3D) Ising models of size L1 ×L1 ×aL1 (a: anisotropy parameter). Paying attention to the a dependence, we have shown that the FSS functions for the magnetization distribution function p(m) at the critical temperature change from a two-peak structure to a single-peak one by increasing or decreasing a from 1. We also study the effects of boundary conditions on the FSS functions for the anisotropic 3D Ising models.